Mathematically in-depth textbook for QM course

[lizzie96']

I'm trying to decide between Dirac, Shankar, Mandl, Griffiths, Gasiorowicz, and Sakurai for an undergrad QM course. It is the first "proper" quantum course after a basic introduction in the modern physics class, but apparently it is particularly mathematically challenging, so I'm looking for a book that is rigourous/difficult/in-depth. Which would you say is the best of these for getting a deep mathematical understanding?

Thanks for any advice!

 

[micromass]

Ballentine is very good to get a rigorous understanding.
But the question is whether you want a first quantum book to be rigorous. It might not be the best idea.

 

[lizzie96']

Thanks, this looks like a good book. It seems like it covers most of the topics in my course, but I'm not sure about peturbation theory- does Ballentine cover that at all?

I'm looking for a rigourous book partly because I am interested in learning more about ideas like Hilbert spaces, but also because the course is specifically aimed at Mathematical Physics students so will have a strong focus on the maths side.

 

[dfan]

I really liked Hall's Quantum Theory for Mathematicians as a supplementary text, as it had clear discussions of the formal issues that "regular" quantum mechanics textbook like to sweep under the rug. I'm not sure how good it would be as your only book.

 

[snatchingthepi]

Literally any of the texts above will serve you purpose - less so with Griffiths. I would personally say use Shankar of those above, but would encourage you to check out Zettili's book.

 

[lizzie96']

Thanks for the suggestions, the Quantum Theory for Mathematicians has exactly the material I was looking for.

 

[JorisL]

My second course in QM used the book by Basdevant and Dalibard.
I quite liked it, its more mathematical than Griffiths but still easy enough for a first course.

 

[verty]

Thanks for the suggestions, the Quantum Theory for Mathematicians has exactly the material I was looking for.

Would it help to read an easier book in addition? I mean, would that not save time? I'm thinking you want to get the most learned before the class starts, this seems to be your aim, to do really well in it.

I recall you are a high achiever in physics, so it's perfectly fine if you are at the required level for that book already, which certainly may be the case.

 

[atyy]

Quantum Mechanics and Quantum Field Theory: A Mathematical Primer
Jonathan Dimock
https://www.amazon.com/dp/1107005094/?tag=pfamazon01-20

 

[micromass]

Hall's book is excellent and one of my favorites. But it is a math book, not a physics book. It does very little physics. It usually just throws the result of the physics out there without motivation, and continues with the mathematical derivations. It is not meant as a first quantum text and should not be used as such.

 

[SgrA*]

I've recently started reading Shankar's book. I'm still in the first chapter, where he first prepares you for the math. On the basis of the first chapter, I'd highly recommend that book: clear explanations, adequate (but not excessive) examples, and in text exercises with gradually increasing difficulty (though it doesn't go beyond a level, at least in the first chapter), which is a big confidence boost.

 

[bill2018]

Dirac is the best one. You have to study path integrals as well.